Monday, September 3, 2012

What is a good textbook?

First of all, there are things a textbook cannot do well, as Dan Meyer points out. A textbook can't wait for student responses in order to find out how helpful it might need to be. Nor can it show you a video of a mathematically-relevant situation. Another sort of problem with textbooks is that inexperienced teachers follow them too closely, and students believe them too readily. 'Question authority' is a pretty good attitude to bring to mathematics, and textbook use does not promote that.

But perhaps, like me, you still want a textbook to offer your students as a one-stop resource for the material you'll be thinking together about in the course. For me, the most important function of the textbook is providing homework problems for my (college) students to use to practice. I also want the mathematical progression of ideas to be recorded somewhere that the students can easily access.

So what makes a good textbook?

At the least, it needs to:
  • do the math properly,
  • be written in good pedagogical style,
  • provide problems that progress from simple (so the students who want to learn the ideas through the problems can) to deeply thought-provoking, including problems that address whatever twists and turns can come up with the material.
  • ??   (What other criteria would you add?)

I told my pre-calc students I'd help them get print copies of one of the open source books I listed, with just the sections they'll need included. But I'm not particularly happy with either one. One thing I do like is that the personalities of the author teams shine through in both of them. (1 pedagogical point earned.)

Here are a few of the things I noticed:

Stitz and Zeager seem to be going for better mathematical reasoning than the commercial textbooks. On page 11:

... the distance formula. Mostly I like what they're doing here. (Many texts treat it as separate from the Pythagorean theorem, which makes me cringe.) But I would not ask 'Do you remember why ...' here. I'd ask if they know why, understand why, or can figure out why. Remembering is for factoids, and why questions should not be thought of as having that sort of answer. I'm reminded of my post on teaching for understanding. Just as the word 'understand' can have deeper and shallower meanings, so can the word 'why'.

Also the use of 'extract' is a bit archaic. It refers to the process used before calculators (bc?) for finding square roots. Nowadays we 'take' the square root of both sides.

Lippman & Rasmussen are probably less likely to include an archaic term like 'extract', but they have other problems. On page 158, in a list of 6 vocabulary words referring to polynomials, they include:
A term of the polynomial is any one piece of the sum, that is any aixi. Each individual term is a transformed power function.

Does 'piece' do anything to define 'term'? When I'm teaching, I sometimes say 'chunk' myself, but I think we do this because we see the terms as standing separately. Our students don't yet see that. So I try to always add in something more helpful like 'terms are separated by a plus or minus'. If you're going to define things in a math book, your definition must give more information than the original word did. 'Any aixi' does that, by example, but a definitional phrase would be helpful.

On the next page, they say:

For any polynomial, the long run behavior of the polynomial will match the long run behavior of the leading term.
They give no indication of why this is true. I do not want to encourage students to think of math as a bunch of  little bits and pieces strung together with no rhyme or reason. Really, it's just the opposite - one huge coherent edifice, full of beauty and mystery. I want students to try to figure out things like long run behavior, based on what they already know.

From the little bit of checking I've done, I'm guessing I prefer having students use the Stitz & Zeager, even though the Lippman & Rusmussen may have more cool problems. I like how Stitz and Zeager write, and the feel they give is usually one of reasoning things out. I'll go with it, and maybe I can send them my suggestions for improvements. (Yeay for open source.)

Thinking about all this makes me want to write my own textbook. That's probably way more work than I want to take on, but I do like writing about math. Maybe some day...


  1. I spent a lot of time this summer reading and thinking about SBG. Then when I sat down to put some stuff on paper, I was all over the place!! I wasted 2-3 days trying to piece together different resources only to give up each time. Then it dawned on me to start with my textbook!! I really dislike our textbook for same reasons I dislike other textbooks (verbose, contrived, dry), so the idea of starting with the text never occurred to me. But it SAVED me this time because it had a concrete pacing that almost makes sense. It was good to use it like the verticals on a ladder, then I used other sources to create the rungs. Yes, the textbook is definitely good for homework skill problems; I'd hate to have to come up with different quadratic equations for kids to solve!

  2. That's funny. For calculus, I definitely did not want to use the rough structure of the textbook. (Almost all of them start with limits. I wanted to start with the coolness of the derivative.) But I'll let the textbook offer some of the explanations. (So far, we haven't used it at all. But in 2 weeks, we'll be using it extensively.)

  3. A good textbook:

    - Has examples, counter-examples and non-examples for all major statements (theorems, lemmas, definitions).

    - Is laid out with clues for visual and sequential people to easily find pieces of text they need to reference at each moment. The text itself is sliced into chunks of appropriate size and of consistent types and styles.

    - Has appropriate clues supporting (work)flow. Namely, indicates where to read slowly, where to pause and exercise, and where to possibly skip some of the content. It also provides tools for faster and slower learners, and for several levels of learners (casual to hardcore).

    - Is made with love and care. This has to be fractal. The authors must love every problem, but also the chapter sequencing and connections between themes. Big things and small have to show love and care. You can always, always tell.

  4. From my experiences polling my students, a good textbook is one that my students will use. To me, it doesn't matter if the book has great examples and/or explanations - if the students won't use the text, what good does it do them?

    I'm definitely guilty of putting most of the information my students need on PowerPoint slides which means that they can ignore the text if they attend every class and follow along.

    Instead of a textbook for Calculus I, I would prefer a book of suitable in class activities for the course that I could use! For whatever reason, my creative juices rarely flow when it comes to designing Calc I activities.

  5. FOR, the Boelkins textbook is mainly activities. You might like it. I've been using quite a few of them.

  6. >Has examples, counter-examples and non-examples for all major statements (theorems, lemmas, definitions).

    Maria, I'm going to think about that idea. I don't think any textbooks do this all the time. I don't think I do, either. I'll try to keep it in mind.


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